I could do an universe explanation to further explain this training codification (another move by the ilKhan perhaps to further Clan unity?) and the Nova Cat decision to alter their training to focus more on their mysticism.
The Horses are fairly straight forward and mostly canonical with Colt making sense as their trainee appearing in FM Crusader Clans. Their instructors being addressed as Wranglers comes from the BC story "A Living Epitaph" by Philip Lee and it does make a great deal of sense given its meaning. A Herd Cluster for a training formation also just seems right but is not from a canon source. Master Arminas referred to the Clan as a whole several times in his Quicksilver submissions which is canon enough for me.
The only two Clans who have fairly similar names for their training institutions are the Wolves and Coyotes. Their canine similarity is matched by their close relationship both politically and militarily. I flipped their trainee names with Coyotes claiming Whelps and Wolves getting Pups. Packmaster is the canon term for Coyote trainers but it fits the Wolves well too. While a Pack Cluster for their training formation seems right. Perhaps both Clans do a certain amount of cross training as well which could range from personnel exchanges to sparring exercises.
I will detail other Clans a bit later.